The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1 X^2  1  1  0  1  1  1  X X^2  0  0
 0  X  0  0  0  X X^2+X X^2+X  0  0 X^2 X^2  X  X  X X^2+X X^2+X  0  X X^2+X X^2+X X^2  0 X^2 X^2  0  X  0  X X^2  X  X X^2+X  0 X^2 X^2  X X^2+X  0  0 X^2  X X^2 X^2+X  0 X^2+X  X  X  X X^2+X X^2  0  X  X  0  0  X X^2 X^2 X^2 X^2 X^2+X  0 X^2+X  0  X  0
 0  0  X  0  X  X  X X^2 X^2  0 X^2+X  X  X  X  0  0 X^2+X X^2  X  0  0 X^2+X  X  0 X^2+X X^2+X X^2  0 X^2+X  0  X  0  X X^2 X^2 X^2+X X^2 X^2+X  X X^2 X^2  0  X  X X^2+X X^2+X  0  0 X^2 X^2  0  0  X  0 X^2 X^2+X X^2+X X^2+X  0 X^2  X  X X^2  0 X^2  X  X
 0  0  0  X  X  0  X  X  X  0  X  0 X^2 X^2+X X^2+X X^2 X^2+X X^2  0  X  0  0 X^2+X X^2+X X^2 X^2+X  0 X^2+X  X  0 X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2+X X^2+X  0 X^2  0 X^2+X X^2 X^2+X  X  X X^2  0  X X^2+X  0 X^2  0  0  0 X^2+X  X  X X^2 X^2 X^2+X  0 X^2  X X^2
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+140x^62+143x^64+272x^66+200x^68+162x^70+29x^72+62x^74+8x^76+2x^78+2x^80+2x^82+1x^120

The gray image is a linear code over GF(2) with n=268, k=10 and d=124.
This code was found by Heurico 1.16 in 46.5 seconds.